Metatheory

A metatheory or meta-theory is a theory whose subject matter is some theory. All fields of research share some meta-theory, regardless whether this is explicit or correct. In a more restricted and specific sense, in mathematics and mathematical logic, metatheory means a mathematical theory about another mathematical theory.

This article is about theories about theories. For the concept in logic, see Metatheorem.

The following is an example of a meta-theoretical statement by Stephen Hawking:

Any physical theory is always provisional, in the sense that it is only a hypothesis; you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory.[1]

Meta-theoretical investigations are generally part of the philosophy of science. Also a metatheory is an object of concern to the area in which the individual theory is conceived.

Taxonomy

Examining groups of related theories, a first finding may be to identify classes of theories, thus specifying a taxonomy of theories.

Psychology

Use of metatheory to "provide a rich source of concepts out of which theories and methods emerge".[2]

Social research

Found to be "infrequently discussed by management scholars and researchers" (Tsoukas, 1994) and almost altogether neglected (Fleetwood, 2007b).

An object of analysis within management sub-fields of study: arguments in favor of the epistemological suitability of case research, and examinations of postmodernist ontological and epistemological or realist perspective (e.g., Jones & Bos,2007;Westwood & Clegg, 2003).

Reflections on theory include the Academy of Management Review's 1989 and 1999 fora on‘‘theory building and improving’’ and ‘‘theory testing’’ (Langley, 1999;Poole & Van de Ven, 1989;Tsang & Kwan, 1999;Van de Ven, 1989;Weick,1989; e.g., Weick, 1999;Whetten, 1989) and a forum on ‘‘what theory isnot’’ (DiMaggio, 1995;Sutton & Staw, 1995;Weick, 1995) and Astley’s(1985) paper in the Administrative Science Quarterly.[3]

In mathematics

Introduced in 20th-century philosophy as a result of the work of the German mathematician David Hilbert, who in 1905 published a proposal for proof of the consistency and completeness of mathematics, creating the field of metamathematics. His hopes for the success of this proof were dashed by the work of Kurt Gödel, who in 1931, used his incompleteness theorems to prove this goal of consistency and completeness to be unattainable. Nevertheless, his program of unsolved mathematical problems, out of which grew this metamathematical proposal, continued to influence the direction of mathematics for the rest of the 20th century.

The study of metatheory became widespread during the rest of that century by its application in other fields, notably scientific linguistics and its concept of metalanguage.

A metatheorem is defined as: "a statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule" known as the duality law or duality principle or by transferring it to another area (from the theory of categories to the theory of groups) or to another context within the same area (from linear transformations to matrices).[4]

Sociology

https://www.researchgate.net/publication/317585884_Metatheory_and_knowledge_organization Examines four types of metatheoretical work: including metatheorizing in order to better understand theory (Mu).

gollark: Not with a bang, or a whimper, but an `inet_aton()`.
gollark: However, they are to.
gollark: Suuuuuuure.
gollark: This is due to C bad, and linked lists being easier than an actually good datastructure.
gollark: Imagine having functions returning linked lists.

See also

References
  1. Stephen Hawking in A Brief History of Time
  2. https://www.researchgate.net/publication/284564323_Meta-theories_theories_and_concepts_in_the_study_of_development
  3. https://www.researchgate.net/publication/228300432_Meta-Theories_in_Research_Positivism_Postmodernism_and_Critical_Realism
  4. Barile, Margherita. "Metatheorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/Metatheorem.html
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